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1 year ago

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There are twelve shirts in your closet, five blue and seven green. Four of the blue shirts and one of the green shirts fit well.

The others are too big. You randomly select a shirt to wear. It is blue or is too big. Find the probability of this occuring

1 answer:

uranmaximum [27]1 year ago

7 0

Answer:

P (blue or too big) = 11 / 12

Explanation:

A two way table permits to represent the situation clearly and find the answser is an easy way.

The two way table is that results from the given information is:

Initial information:

Blue Green Total

Fit well 4 1 ?

Too big ? ? ?

Total 5 7 12

Now by subtraction and addition you can fill the unknown fields:

Blue Green Total

Fit well 4 1 5

Too big 1 6 7

Total 5 7 12

Now, you can see that there are 5 blue and 7 too big shirts, but the total number of them is 5 + 7 - 1 (because one of the too big shirts is also blue).

Then, the number of shirts being blue or too big is 5 + 7 - 1 = 11.

And the probability is :

P(blue or too big) = number of blue or too big / total number of shirts

P (blue or too big) = 11 / 12 ← answer

You can also realize that there is only 1 green shirt that fits well, and that is the only option of not being blue of too big, so 1 /12 is the probability of not being blue or too big, and its complement (being blue or too big) is 1 - 1/12 = 11 / 12.

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A torch and a battery cost £2.50 altogether. The torch costs £2.00 more than the battery.

Genrish500 [490]

Answer:

$\frac{1}{10}$

Step-by-step explanation:

Let $t$ represent the cost of the torch and $b$ represent the cost of the battery.

The torch and a battery cost £2.50 altogether.

$\Rightarrow t+b=2.50$

The torch costs £2.00 more than the battery.

$\Rightarrow t=b+2.00$

We substitute the second equation into the first equation to get;

$\Rightarrow b+2.00+b=2.50$

$\Rightarrow 2b=2.50-2.00$

£2.50

$\Rightarrow 2b=0.50$

$\Rightarrow b=0.25$

The price of the battery is £0.25

We express this as a fraction of the total cost which is £2.50 to get;

$\frac{0.25}{2.5}=\frac{1}{10}$

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Points A(-2,3), B(-5,-4), and C(2,-1) form triangle ABC on a coordinate plane. What is the area of this triangle in square units

Veseljchak [2.6K]

1. Draw an accurate picture of the triangle in the coordinate axes, as shown in the attached picture.<span>

<span>2. Circumscribe a rectangle about the triangle, as shown in the picture. The coordinates of the points M, N, T are easily identifiable as shown in the picture.</span>

<span>3. The area of the triangle ABC is The area of the rectangle - Area 1- Area 2- Area 3.</span>

Area 1 = 1/2(3*7)=21/2
Area 2 = 1/2(4*4)=1/2*16=8
<span>Area 3 = 1/2( 3*7)=21/2</span>

<span>Area 1+Area 2+Area 3=21/2+21/2+8=21+8=29 (units squared)</span>

<span>Area rectangle= 7*7=49 (units squared)</span>

<span>Answer: Area of triangle is 20 units squared.</span></span>

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n 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to comp

Zarrin [17]

Answer:

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Step-by-step explanation:

For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

97.4% finished:

This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that $p = 0.026$

100 runners are chosen at random

This means that $n = 100$

Find the probability that at least 5 of them did not finish the marathon

This is:

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718$

$P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916$

$P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531$

$P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207$

$P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199$

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

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we know that

If line b is perpendicular to line a, and line c is perpendicular to line a,

then

line b and line c are parallel

and two lines parallel have the same slope

so

<u>Find the slope of the line b</u>

Let

$A(-3,-2)\\B(2,3)$

The formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

$(x1,y1)=(-3,-2)\\(x2,y2)=(2,3)$

substitute

$m=\frac{(3+2)}{(2+3)}$

$m=\frac{(5)}{(5)}$

$m=1$

therefore

<u>the answer is</u>

<u>the slope of the line c is</u>

$mc=1$

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Oksana_A [137]

The corresponding sides of the model and the actual bridge are in proportion because the two solids are similar.

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